PhD's web site dcfun Publications MathExp Team


The Maple dcfun package aims at deal with
linear Mahler operators/equations
linear divide-and-conquer recurrences.
Currently, dcfun provides solutions of type rational function, formal power series, formal Puiseux series among others for homogeneous linear Mahler equations. Also it finds first-order right-hand factors of linear Mahler operators.




0.0.0 operations on operators, solving of Mahler equations

The search for solutions of linear Mahler equations in some classes of functions is motivated by two reasons. First there is a general trend to solve functional equations, that has begun with the work of Liouville (1833) about differential equations and was continued by Abramov (1989) for recurrences. Particularly the search for rational solutions is a building block for other algorithms (like summation algorithms). Next Mahler equations are related to transcendence issues. This standpoint comes from Mahler's work (1929, 1930) about this topic. More recently, several works (Adamcwezski and Faverjon, 2017; Dreyfus, Hardouin, and Roques, 2018, among others) provide criteria to recognize if an object is transcendental and these criteria are based on the existence of solutions of a given type for some Mahler equations.